Costa also made another goal before coming off with 10 minutes left to rest what currently passes as the most valuable treasure at Stamford Bridge - that fragile left hamstring.
Mourinho had spent the eve of the match bemoaning how he was powerless to stop Spain calling up Costa in between Chelsea's matches, even though he evidently feels that only a sustained period of rest can guarantee the player recovers full fitness.
The injury, which flared up again in the last round of European Championship qualifying matches, gnaws away at Costa to the point that he cannot play two complete games in four days.
It was a point that Mourinho, looking forward to Chelsea's Champions League encounter with Sporting Lisbon this week, reiterated after his heroics against Villa.
The Portuguese coach manager suggested it was now in both club and country's interests to give Costa a break from Spain's matches against Macedonia and Luxembourg in October.
"If he doesn't go to the national team and stays here for 15 days, just in treatment, recovering and making the muscle stronger, he has the perfect chance to be in top condition for Chelsea and the national team," said Mourinho.
"Between matches, he's doing almost nothing, just resting and recovering from the tight muscle he has every time he accumulates fatigue."
There was little else to concern Mourinho, though, as he celebrated a familiar outcome to his 250th game at the club.
Chelsea's Brazil midfielder Oscar looked rejuvenated as he scored his second goal in a week, leaving Mourinho to enthuse: "His performance was good; he was in important areas of our game and the connection between him, (Nemanja) Matic and (Cesc)Fabregas was good."
With Willian scoring the third, after good work from Costa, it all left Mourinho contemplating a fine afternoon's work.
"I'm happy. Overall, it was a very good performance," he said, insisting Chelsea's three point lead at the top was merely "a little bit of a space that gives you a good feeling."
(Editing by Ken Ferris)
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